Question

How old is a mammoth's tusk if 25 percent of the original C-14 remains in the sample, if the half-life of C-14 is 5730 years?

Answer 1

Answer:

11,554.53 years old is a mammoth's tusk.

Explanation:

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{5730 year}= 0.000120 year^{-1}$

$N=N_o\times e^{-\lambda t}$

N = amount left after time t = $25\%$ of a = 0.25 a

$N_o$ = initial amount  = a

$\lambda$ = rate constant

t= time = ?

$\log[N]=\log[N_o]-\frac{\lambda t}{2.303}$

$\log\frac{N}{N_o}=-\frac{\lambda\times t}{2.303}$

t = 11,554.53 years

11,554.53 years old is a mammoth's tusk.

Answer 2

Explanation:

11,554.53 years old is a mammoth's tusk.

Explanation:

\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{5730 year}= 0.000120 year^{-1}λ=

t

2

1

0.693

=

5730year

0.693

=0.000120year

−1

N=N_o\times e^{-\lambda t}N=N

o

×e

−λt

N = amount left after time t = 25\%25% of a = 0.25 a

N_oN

o

= initial amount = a

\lambdaλ = rate constant

t= time = ?

\log[N]=\log[N_o]-\frac{\lambda t}{2.303}log[N]=log[N

o

]−

2.303

λt

\log\frac{N}{N_o}=-\frac{\lambda\times t}{2.303}log

N

o

N

=−

2.303

λ×t

t = 11,554.53 years

11,554.53 years old is a mammoth's tusk.